Figure 1.
Optimal solutions in the first example
-
Previous Article
An optimal algorithm for the obstacle neutralization problem
- JIMO Home
- This Issue
-
Next Article
Some characterizations of robust optimal solutions for uncertain fractional optimization and applications
April
2017, 13(2): 825-834.
doi: 10.3934/jimo.2016048
Robust design of sensor fusion problem in discrete time
| 1. | LinJiang Middle School, KaiZhou District, Chongqing, China |
| 2. | College of Mathematical Sciences, Chongqing Normal University, Chongqing, China |
In this paper, we consider a robust sensor scheduling problem which estimates the state of an uncertain process based on measurements obtained by a given set of noisy sensors, where the measurements of sensors are subject to external interference uncertainties. We formulate this problem into a minimax optimal control problem, which is equivalent to a semi-infinite programming problem with a dynamic system. A discretization method is used to solve this problem, where the computation is very large scale in general. We propose an approximation method to reduce the computational complexity. For illustration, two numerical examples are solved.
Keywords:
Robust sensor fusion design,
semi-infinite programming.
Mathematics Subject Classification:
Primary: 49M37; Secondary: 90C34.
Citation:
Xiao Lan Zhu, Zhi Guo Feng, Jian Wen Peng. Robust design of sensor fusion problem in discrete time. Journal of Industrial and Management Optimization,
2017, 13
(2)
: 825-834.
doi: 10.3934/jimo.2016048
![]()
References:
| [1] |
T. Abburi and S. Narasimhan,
Optimal sensor scheduling in batch processes using convex relaxations and tchebycheff systems theory, IEEE Transactions on Automatic Control, 59 (2014), 2978-2983.
doi: 10.1109/TAC.2014.2351692. |
| [2] |
Z. L. Deng, Y. Gao, L. Mao, Y. Li and G. Hao,
New approach to information fusion steady-state Kalman filtering, Automatica, 41 (2005), 1695-1707.
doi: 10.1016/j.automatica.2005.04.020. |
| [3] |
Z. G. Feng, K. L. Teo and Y. Zhao,
Branch and bound method for sensor scheduling in discrete time, Journal of Industrial and Management Optimization, 1 (2005), 499-512.
doi: 10.3934/jimo.2005.1.499. |
| [4] |
Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan,
Optimal fusion of sensor data for Kalman filtering, Discrete and ContinuousDynamical Systems, 14 (2006), 483-503.
|
| [5] |
Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan,
Optimal fusion of sensor data for discrete Kalman filtering, Dynamic Systems and Applications, 16 (2007), 393-406.
|
| [6] |
Z. G. Feng, K. L. Teo and V. Rehbock,
Hybrid method for a general optimal sensor scheduling problem in discrete time, Automatica, 44 (2008), 1295-1303.
doi: 10.1016/j.automatica.2007.09.024. |
| [7] |
F. N. Grigor'ev and N. A. Kuznetsov,
Control of the observation process in continuous systems, Problems of Control and Information Theory, 6 (1977), 181-201.
|
| [8] |
F. N. Grigor'ev,
About the control of information processing in discrete automatic systems, Automation and Remote Control, 43 (1982).
|
| [9] |
H. Kushner,
On the optimum timing of observations for linear control systems with unknown initial state, IEEE Transactions on Automatic Control, 9 (1964), 144-150.
|
| [10] |
H. W. J. Lee, K. L. Teo and L. S. Jennings,
Control parametrization enhancing techniques for optimal discrete-valued control problems, Automatica, 35 (1999), 1401-1407.
doi: 10.1016/S0005-1098(99)00050-3. |
| [11] |
H. W. J. Lee, K. L. Teo and A. E. B. Lim,
Sensor scheduling in continuous time, Automatica, 37 (2001), 2017-2023.
doi: 10.1016/S0005-1098(01)00159-5. |
| [12] |
Y. Li, L. W. Krakow, E. K. Chong and K. N. Groom,
Approximate stochastic dynamic programming for sensor scheduling to track multiple targets, Digital Signal Processing, 19 (2009), 978-989.
doi: 10.1016/j.dsp.2007.05.004. |
| [13] |
J. L. Liu, Y. Sun, J. Yang, W. Y. Liu and W. M. Chen,
Optimal sensor scheduling for hybrid estimation, Journal of Central South University, 20 (2013), 2186-2194.
doi: 10.1007/s11771-013-1723-4. |
| [14] |
B. M. Miller,
Observation control for discrete-continuous stochastic systems, IEEE Transactions on Automatic Control, 45 (2000), 993-998.
doi: 10.1109/9.855571. |
| [15] |
V. Malyavej, I. R. Manchester and A. V. Savkin,
Precision missile guidance using radar/multiple-video sensor fusion via communication channels with bit-rate constraints, Automatica, 42 (2006), 763-769.
doi: 10.1016/j.automatica.2005.12.024. |
| [16] |
A. S. Matveev and A. V. Savki,
Optimal state estimation in networked systems with asynchronous communication channels and switched sensors, Journal of optimization theory and applications, 128 (2006), 139-165.
doi: 10.1007/s10957-005-7562-1. |
| [17] |
A. V. Savkin, R. J. Evans and E. Skafidas,
The problem of optimal robust sensor scheduling, Systems Control Lett., 43 (2001), 149-157.
doi: 10.1016/S0167-6911(01)00086-X. |
| [18] |
S. L. Sun,
Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother, Automatica, 41 (2005), 2153-2159.
doi: 10.1016/j.automatica.2005.06.014. |
| [19] |
K. L. Teo, C. Goh and K. Wong,
A Unified Computational Approach to Optimal Control Problems, copublished in the United States with John Wiley & Sons, Inc., New York, 1991. |
| [20] |
C. Z. Wu, K. L. Teo and X. Y. Wang,
Minimax optimal control of linear system with input-dependent uncertainty, Journal of the Franklin Institute, 351 (2014), 2742-2754.
doi: 10.1016/j.jfranklin.2014.01.012. |
| [21] |
C. Z. Wu, K. L. Teo and S. Y. Wu,
Min-max optimal control of linear systems with uncertainty and terminal state constraints, Automatica, 49 (2013), 1809-1815.
doi: 10.1016/j.automatica.2013.02.052. |
| [22] |
M. Yavuz and D. Jeffcoat, An analysis and solution of the sensor scheduling problem, In
Advances in Cooperative Control and Optimization, Springer Berlin Heidelberg, 369 (2007),
167–177.
doi: 10.1007/978-3-540-74356-9_10. |
show all references
References:
| [1] |
T. Abburi and S. Narasimhan,
Optimal sensor scheduling in batch processes using convex relaxations and tchebycheff systems theory, IEEE Transactions on Automatic Control, 59 (2014), 2978-2983.
doi: 10.1109/TAC.2014.2351692. |
| [2] |
Z. L. Deng, Y. Gao, L. Mao, Y. Li and G. Hao,
New approach to information fusion steady-state Kalman filtering, Automatica, 41 (2005), 1695-1707.
doi: 10.1016/j.automatica.2005.04.020. |
| [3] |
Z. G. Feng, K. L. Teo and Y. Zhao,
Branch and bound method for sensor scheduling in discrete time, Journal of Industrial and Management Optimization, 1 (2005), 499-512.
doi: 10.3934/jimo.2005.1.499. |
| [4] |
Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan,
Optimal fusion of sensor data for Kalman filtering, Discrete and ContinuousDynamical Systems, 14 (2006), 483-503.
|
| [5] |
Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan,
Optimal fusion of sensor data for discrete Kalman filtering, Dynamic Systems and Applications, 16 (2007), 393-406.
|
| [6] |
Z. G. Feng, K. L. Teo and V. Rehbock,
Hybrid method for a general optimal sensor scheduling problem in discrete time, Automatica, 44 (2008), 1295-1303.
doi: 10.1016/j.automatica.2007.09.024. |
| [7] |
F. N. Grigor'ev and N. A. Kuznetsov,
Control of the observation process in continuous systems, Problems of Control and Information Theory, 6 (1977), 181-201.
|
| [8] |
F. N. Grigor'ev,
About the control of information processing in discrete automatic systems, Automation and Remote Control, 43 (1982).
|
| [9] |
H. Kushner,
On the optimum timing of observations for linear control systems with unknown initial state, IEEE Transactions on Automatic Control, 9 (1964), 144-150.
|
| [10] |
H. W. J. Lee, K. L. Teo and L. S. Jennings,
Control parametrization enhancing techniques for optimal discrete-valued control problems, Automatica, 35 (1999), 1401-1407.
doi: 10.1016/S0005-1098(99)00050-3. |
| [11] |
H. W. J. Lee, K. L. Teo and A. E. B. Lim,
Sensor scheduling in continuous time, Automatica, 37 (2001), 2017-2023.
doi: 10.1016/S0005-1098(01)00159-5. |
| [12] |
Y. Li, L. W. Krakow, E. K. Chong and K. N. Groom,
Approximate stochastic dynamic programming for sensor scheduling to track multiple targets, Digital Signal Processing, 19 (2009), 978-989.
doi: 10.1016/j.dsp.2007.05.004. |
| [13] |
J. L. Liu, Y. Sun, J. Yang, W. Y. Liu and W. M. Chen,
Optimal sensor scheduling for hybrid estimation, Journal of Central South University, 20 (2013), 2186-2194.
doi: 10.1007/s11771-013-1723-4. |
| [14] |
B. M. Miller,
Observation control for discrete-continuous stochastic systems, IEEE Transactions on Automatic Control, 45 (2000), 993-998.
doi: 10.1109/9.855571. |
| [15] |
V. Malyavej, I. R. Manchester and A. V. Savkin,
Precision missile guidance using radar/multiple-video sensor fusion via communication channels with bit-rate constraints, Automatica, 42 (2006), 763-769.
doi: 10.1016/j.automatica.2005.12.024. |
| [16] |
A. S. Matveev and A. V. Savki,
Optimal state estimation in networked systems with asynchronous communication channels and switched sensors, Journal of optimization theory and applications, 128 (2006), 139-165.
doi: 10.1007/s10957-005-7562-1. |
| [17] |
A. V. Savkin, R. J. Evans and E. Skafidas,
The problem of optimal robust sensor scheduling, Systems Control Lett., 43 (2001), 149-157.
doi: 10.1016/S0167-6911(01)00086-X. |
| [18] |
S. L. Sun,
Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother, Automatica, 41 (2005), 2153-2159.
doi: 10.1016/j.automatica.2005.06.014. |
| [19] |
K. L. Teo, C. Goh and K. Wong,
A Unified Computational Approach to Optimal Control Problems, copublished in the United States with John Wiley & Sons, Inc., New York, 1991. |
| [20] |
C. Z. Wu, K. L. Teo and X. Y. Wang,
Minimax optimal control of linear system with input-dependent uncertainty, Journal of the Franklin Institute, 351 (2014), 2742-2754.
doi: 10.1016/j.jfranklin.2014.01.012. |
| [21] |
C. Z. Wu, K. L. Teo and S. Y. Wu,
Min-max optimal control of linear systems with uncertainty and terminal state constraints, Automatica, 49 (2013), 1809-1815.
doi: 10.1016/j.automatica.2013.02.052. |
| [22] |
M. Yavuz and D. Jeffcoat, An analysis and solution of the sensor scheduling problem, In
Advances in Cooperative Control and Optimization, Springer Berlin Heidelberg, 369 (2007),
167–177.
doi: 10.1007/978-3-540-74356-9_10. |
Figure 2.
he cost function values in the first example
Figure 3.
Optimal solutions of the second example
| [1] |
Yanqun Liu, Ming-Fang Ding. A ladder method for linear semi-infinite programming. Journal of Industrial and Management Optimization, 2014, 10 (2) : 397-412. doi: 10.3934/jimo.2014.10.397 |
| [2] |
Cheng Ma, Xun Li, Ka-Fai Cedric Yiu, Yongjian Yang, Liansheng Zhang. On an exact penalty function method for semi-infinite programming problems. Journal of Industrial and Management Optimization, 2012, 8 (3) : 705-726. doi: 10.3934/jimo.2012.8.705 |
| [3] |
Ke Su, Yumeng Lin, Chun Xu. A new adaptive method to nonlinear semi-infinite programming. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1133-1144. doi: 10.3934/jimo.2021012 |
| [4] |
Zhi Guo Feng, Kok Lay Teo, Volker Rehbock. A smoothing approach for semi-infinite programming with projected Newton-type algorithm. Journal of Industrial and Management Optimization, 2009, 5 (1) : 141-151. doi: 10.3934/jimo.2009.5.141 |
| [5] |
Jinchuan Zhou, Changyu Wang, Naihua Xiu, Soonyi Wu. First-order optimality conditions for convex semi-infinite min-max programming with noncompact sets. Journal of Industrial and Management Optimization, 2009, 5 (4) : 851-866. doi: 10.3934/jimo.2009.5.851 |
| [6] |
Jinchuan Zhou, Naihua Xiu, Jein-Shan Chen. Solution properties and error bounds for semi-infinite complementarity problems. Journal of Industrial and Management Optimization, 2013, 9 (1) : 99-115. doi: 10.3934/jimo.2013.9.99 |
| [7] |
Burcu Özçam, Hao Cheng. A discretization based smoothing method for solving semi-infinite variational inequalities. Journal of Industrial and Management Optimization, 2005, 1 (2) : 219-233. doi: 10.3934/jimo.2005.1.219 |
| [8] |
Z. G. Feng, Kok Lay Teo, N. U. Ahmed, Yulin Zhao, W. Y. Yan. Optimal fusion of sensor data for Kalman filtering. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 483-503. doi: 10.3934/dcds.2006.14.483 |
| [9] |
Azhar Ali Zafar, Khurram Shabbir, Asim Naseem, Muhammad Waqas Ashraf. MHD natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 1007-1015. doi: 10.3934/dcdss.2020059 |
| [10] |
Xiaodong Fan, Tian Qin. Stability analysis for generalized semi-infinite optimization problems under functional perturbations. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1221-1233. doi: 10.3934/jimo.2018201 |
| [11] |
Rafael del Rio, Mikhail Kudryavtsev, Luis O. Silva. Inverse problems for Jacobi operators III: Mass-spring perturbations of semi-infinite systems. Inverse Problems and Imaging, 2012, 6 (4) : 599-621. doi: 10.3934/ipi.2012.6.599 |
| [12] |
Igor Chueshov. Remark on an elastic plate interacting with a gas in a semi-infinite tube: Periodic solutions. Evolution Equations and Control Theory, 2016, 5 (4) : 561-566. doi: 10.3934/eect.2016019 |
| [13] |
Roman Chapko, B. Tomas Johansson. An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions. Inverse Problems and Imaging, 2008, 2 (3) : 317-333. doi: 10.3934/ipi.2008.2.317 |
| [14] |
Meixia Li, Changyu Wang, Biao Qu. Non-convex semi-infinite min-max optimization with noncompact sets. Journal of Industrial and Management Optimization, 2017, 13 (4) : 1859-1881. doi: 10.3934/jimo.2017022 |
| [15] |
Atul Kumar, R. R. Yadav. Analytical approach of one-dimensional solute transport through inhomogeneous semi-infinite porous domain for unsteady flow: Dispersion being proportional to square of velocity. Conference Publications, 2013, 2013 (special) : 457-466. doi: 10.3934/proc.2013.2013.457 |
| [16] |
Changzhi Wu, Chaojie Li, Qiang Long. A DC programming approach for sensor network localization with uncertainties in anchor positions. Journal of Industrial and Management Optimization, 2014, 10 (3) : 817-826. doi: 10.3934/jimo.2014.10.817 |
| [17] |
Magdi S. Mahmoud, Omar Al-Buraiki. Robust control design of autonomous bicycle kinematics. Numerical Algebra, Control and Optimization, 2014, 4 (3) : 181-191. doi: 10.3934/naco.2014.4.181 |
| [18] |
Ruotian Gao, Wenxun Xing. Robust sensitivity analysis for linear programming with ellipsoidal perturbation. Journal of Industrial and Management Optimization, 2020, 16 (4) : 2029-2044. doi: 10.3934/jimo.2019041 |
| [19] |
Gang Li, Yinghong Xu, Zhenhua Qin. Optimality conditions for composite DC infinite programming problems. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022064 |
| [20] |
Hui Zhang, Jian-Feng Cai, Lizhi Cheng, Jubo Zhu. Strongly convex programming for exact matrix completion and robust principal component analysis. Inverse Problems and Imaging, 2012, 6 (2) : 357-372. doi: 10.3934/ipi.2012.6.357 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]